Math 240 Notes and Home Work

• Notes on vector spaces
• exponential of 3x3 matrices and Green's function for second order ODE's , by Dr. Powers; the same notes on Dr. Powers's page.
• Vector spaces attached to an m by n matrix
• Notes on how to compute the Jordan form of a given square matrix after you have factored the characteristic polynomial. An algorithm is explained in the notes. If you figured out how to prove that the algorithm indeed computes the Jordan form and write up all the details, you are entitled some extra credits.
• Notes on computing matrix exponentials

• Homework 1, week of January 10
• Homework 2, week of January 15
• Homework 3, week of January 22
• Homework 4, week of January 29
• practice problems before the first in-class midterm exam
• challenge/extra-credit problems on a closed formula for matrix exponential
• Homework 5, week of February 12
• Homework 6, week of February 19
• Homework 7, week of February 26
• Homwwork 8, week of March 12
• practice problems before the second in-class midterm exam
• Homework 9
• Homework 10, week of March 26
• Homework 11, week of April 2
• Homework 12, week of April 9
• Practice problems, April 2018

• Linear plane autonomous systems
• An example of non-linear plane autonomous system
• picture of a limit cycle
• figure 9.10.1 in DELA
• figure 9.10.1 in DELA

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